Have I got this right, your music volume from an external app drops when you start the game?
If you are on Windows 7 (and maybe Vista) read on, otherwise I dunno. W7 has a feature to drop the volume of all other apps when you receive a voip call, it might be deciding L4D voip is a voip call. As the volume drops when you start a game and not before this is the only thing I can think of.
Go to Control Panel, Hardware and Sound, manage audio devices, communications tab and tick "Do nothing".